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postnew [5]
3 years ago
7

PR and PS are tangent to center Q. Find the measurement of angle Q

Mathematics
1 answer:
iVinArrow [24]3 years ago
8 0
Segment PQ bisects the angle P, which means angle QPR has a measure of 21 degrees (which follows from the fact that triangles PQR and PQS are congruent and PR and PS are tangent to the circle).

This then means angle RQP has measure 90 - 21 = 69 degrees.

Angle Q is twice this, so it has measure 138 degrees.
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Find the values of sin2u, cos2u, and tan2u given the figure.
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Givens

y = 2

x = 1

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Cos(u) = x value / hypotenuse = 1/√5

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Solve for sin2u

Sin(2u) = 2*sin(u)*cos(u)

Sin(2u) = 2(\dfrac{1}{\dsqrt{5}} * \frac{2}{\dsqrt{5}} = \dfrac{2}{5}) = 4/5

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Solve for Tan(2u)

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Notes

One: Notice that you would normally rationalize the denominator, but you don't have to in this case.  The formulas are such that they perform the rationalizations themselves.

Two: Notice the sign on the cos(2u). The sin is plus even though the angle (2u) is in the second quadrant. The cos is different. It is about 126 degrees which would make it a negative root (9/25)

Three: If you are uncomfortable with the  tan, you could do fractions.

\text{tan(2u)} = \dfrac{\dfrac{4}{5}}{\dfrac{-3}{5} } =\dfrac{4}{5} *\dfrac{5}{-3} =\dfrac{4}{-3}

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Answer:

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Step-by-step explanation:

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